Mooring apparatus having a free floating buoyant element



June 30, 1970 W ET AL 3,517,399

MOORING APPARATUS HAVING A FREE FLOATING BUOYANT ELEMENT Filed March 4,1966 INVENTORS. MAURICE HOROWITZ AND CLINTON S. MYERS United StatesPatent 0 3,517,399 MOORING APPARATUS HAVING A FREE FLOATING BUOYANTELEMENT Maurice Horowitz and Clinton S. Myers, Fort Wayne, Ind.,assignors to The Magnavox Company, Fort Wayne,

Ind.

Filed Mar. 4, 1966, Ser. No. 531,960 Int. Cl. B63b 21/52 U.S. Cl. 9--8 1Claim ABSTRACT OF THE DISCLOSURE Mooring apparatus is provided with abuoy having optimum submergence and lift, and with a cable havingoptimum strength and length. When anchored in water, the buoy remainsabove the water and near the anchor for an optimum length of time undervarious conditions of the surrounding water and atmosphere.

This invention relates to an improved mooring apparatus having a buoyantelement which is free floating within limits defined by a cable or othertethering means which is anchored at its base or bottom end.

More particularly, the present invention relates to a process forestablishing various structural criteria for producing an optimumcombination of float element and a tethering means for such floatelement and permitting the float element to move within circumscribedbounds.

For various reasons the art has long attempted to produce a flotationsystem which can be readily packaged and transported to a point of useand then fixed at a certain location within an ocean, lake or sea sitefor the purpose of accomplishing, among other things, certain monitoringfunctions. Flotation systems in general have been unsatisfactory andparticularly deep anchored flotation systems for use in deep water inconjunction with oceanographic, communication, military, naval, fisheryand transportation uses have been entirely unreliable because of thelack of processing information tying together cable size, length, orfloat size, etc. For one thing, such systems have uniformly lackedreliability because as the sea state conditions change, the floatelement would frequently break away from its mooring, thus destroyingthe system. In order to prevent such breakaway the flexible mooringelement in the form of a cable, or the like, was made larger but this,in turn, necessitated a larger float, thus increasing the effects ofdrag and inertia for supporting the mooring cable and as a consequence,the flotation systems reached large proportions, making them ditficultto transport while still lacking any satisfactory degree of reliability.The problem was further complicated by the lack of establishing properlimitations on the cable or other mooring element length. For example,if the cable length equaled or substantially equaled the depth of thewater body in which the flotation member was anchored then the strainsdeveloped on the anchoring means by the drag forces on the float becameinordinately high and necessitated too great a size of the anchoringelement to withstand such forces. On the other hand, if the mooringelement was made longer the surface area over which the flotationelement could migrate became so considerable that the informationprovided by the system was rendered indefinite by failing to pinpointthe location of information provided by the system. The severity ofthese problems increases as the desired mooring depth increases.

What is needed, therefore, is a reliably anchored flotation systemadapted for use with scanning sonars, moored beacons, moored telemetersand other such applications.

ice

The present invention allows optimization of all parameters of themoored system thereby providing not only a high degree of reliabilityand long life but also allows the realization of a deep moored minimumweight system which is capable of being easily transported and launchedeven by airborne methods which heretofore has been highly impracticable.

It is one of the important features of the present invention to provideapparatus whereby moored systems can be readily established providingoptimum system results wherein float size is related to a satisfactorycable or other tethering means and in which there is readily establisheda diameter, weight, and length of mooring cable enabling the system towithstand high currents and inertia forces. In providing a system ofthis type, a cable or other tethering element can be so designed that,in relation to a given size and configuration of float, there isproduced a system which is reliably retained in place under sea stateconditions ranging from tranquil to very heavy and which will maintainits assigned monitoring area regardless of the sea state condition orchange of sea state condition.

It is a still further object of the present invention to provideapparatus having a combination float and anchoring system which are sorelated together that the combination can be of whatever size and weightdesired, within ranges, of course, so that the system is readilytransportable yet possesses the necessary structural strength forresisting breaking.

It is an important feature of the present invention that the floatportion of the system has a surface buoyancy such that a portion thereofremains unsubmerged throughout sea state conditions ranging fromtranquil to very heavy so that monitoring can occur and be transmittedsubstantially constantly regardless of the sea state condition.

The present invention is not limited to an environment of sea water; theapparatus is usable for any moored or float system comprised of a liquidsurmounted by a gas. The apparatus may also be equipped, if desired,with sub-surface floats and canisters but it is essential to the presentinvention that the required cable tethering length will exceed the totaldepth so that the float will not impose excessive strain on the cable asit is tended to move by surface current forces. At the same time thecable must not be so excessively long so that the float extends over anexcessive area and provides excessive forces tending to submerge thefloat because of the period of the waves being less than the responsetime supplied by the float buoyancy. It is, of course, necessary thatthe cable float have suflicient slack so that it can maneuver in thewaves without becoming submerged and without imposing excessive forcesupon a taut or short cable (or other tethering means) during suchmaneuvering.

It is, therefore, one of the important accomplishments of the presentinvention to establish a moored system which will satisfy the systemrequirements of: (1) nonsubmergence of the surface float; (2)nonbreaking of the cable or other tethering means; (3) minimum lengthand cross-sectional area of the cable or other tethering means; (4)minimum horizontal displacement of the float from the anchor; and (5)survival in specified currents and winds.

Other objects and features of the present invention will become apparentfrom a consideration of the following description which proceeds withreference to the accompanying drawings, wherein:

FIG. 1 is a schematic view showing a float, a tethering means and anchorand illustrating the various forces and directions of forces which actupon the float;

FIG. 2 illustrates the position of the float in different seaconditions.

Referring now to the drawings, a flotation member designated generallyby reference numeral 10 which floats at the surface 12 of a body ofwater and has a submerged portion and an unsubmerged portion whichremains unsubmerged in sea conditions ranging from tranquil to high seaconditions except those which are extremely turbulent, and then onlytemporarily.

Below the surface of the float is an attachment point 14 for a cable orother flexible member 16 which is secured to point 14 at one end and isattached at the opposite end 18 to an anchor 20 which is fixed at thebottom 22 of the body of water. The buoy or float is subjected to asubstantial number of external forces; these forces influence themovement and flotation of the buoy and such forces must be taken intoaccount in determining whether the float can remain afloat with at leasta portion of it unsubmerged in the various sea rate conditions and alsowhether the float can respond rapidly enough to the sea state conditionsso that its inertia will enable it to respond quickly enough to ride ontop of the Waves. Also, such external forces determine whether or not agiven float is adequately tethered, that is, whether it is held Withinthe strength limitations of the mooring system.

In an analysis of the problem, it is necessary to relate the float sizeand float requirements to the capability of the mooring system to holdthe float within bounds and prevent its breaking away regardless of thesea state conditions.

In order to accomplish these ends, the optimum values of the variousfloat parameters are set forth by simultaneously equating therelationship of the submergence, Y of the float, which is the distancefrom the water level to the lowermost point of the float, the tension T,which is the tension of the cable at its point of attachment with thefloat, and the angle, which is the cable angle at the point ofattachment, all to the drag and lift factors operating on the float,including those parameters affecting the drag due to the water surrents,D as well as those due to air currents, D

The above parameters together with the drag, D per unit length of thecable are further differentially related, in order to establishthe cabledimensions such as the length, L, mass, M, volume, V, and displacement,X, of the float from the anchor for assumed values of the cable tension.The dimensions which result from assuming a given tension are used tobalance the tethering system or anchoring system against the floatsystem and allows the determination of whether the cable is either toolarge and hence too cumbersome, expensive and nontransportable or,conversely, if the cable is too small, in which case the cable will beexcessively long or too weak.

It is found that in the system of the present invention for a float ofgiven configuration immersed at the surface by a fixed amount,specifying the cable tension at the surface uniquely determines thecable angle and the physical dimension of the float. This discoveryenables all portions of the system to be analyzed, varying only oneparameter, namely, that of the cable tension at the surface. The systemonce properly configured can then be disposed within a given area andfunction as a moored scanning sonar, moored beacon, moored telemeter orthe like. The system of the present invention enables the design andcomputational proceeding using the laws of hydrodynamics and opens up asystematic procedure for establishing the cable diameter, weight, andlength and the float size, for a system adapted to withstand highcurrents of both sea and air, and waves.

Previous to the present invention it was virtually impossible to provideany deep anchored system for oceanographic communication, military,naval, fishery and transportation uses and have the system survivereliably over a period of time. The system further establishes the draftpermitted for the float and the cable angle required for developing thenecessary resistance under assumed current and wave conditions whilewithstanding breakage. The length of the cable is designed so that it isgreater than the immersion depth and yet is not so long as to create anexcessively large and hence indefinite monitoring area. In other words,what is rendered is a cable long enough to reduce tautness and allow thefloat to maneuver in the waves while at the same time producing a cableof optimum weight and low volume.

The effect of waves is to tend to submerge the float unless the responsetime supplied by the float buoyancy is sufliciently less than the periodof the waves. The size of the float and the tethering cable must be in abalanced relationship under the various environmental conditions. Suchbalance must result in a float which will not submerge and yet whichwill not be too bulky; the cable must neither be too short and henceoverly taut and large and cause the lack of float maneuverability or betoo long so as to cause indefiniteness in monitoring. The specificproblem then is to provide a system having a tethering cable and floatwhich will neither break the cable nor submerge the float under strongcurrents and high surface waves. These requirements are to be combinedWithin a system embodying minimum Weight and volume of cable. Thisinvention satisfies the requirements of the system as to:

(1) Nonsubmergence of the surface float.

(2) Integrity of the cable.

(3) Small volume to meet packaging requirements.

(4) Minimum horizontal displacement of the float from its anchor.

(5) Survival of the system in specified wind and water currents.

The system (containing floats, canisters, etc. of any size and shape andindependently of the gas which is above any kind of fluid subject to thecurrents, wind and waves) can be provided as follows:

STEP 1 Establishment of the relationship for optimum submergence, Y ofthe floatz' The submergence, Y is the distance from the top of theliquid to the bottom of the float 10. The optimum submergence will fallbetween the two extremes of no submergence and total submergence.Analysis of these two extremes are as follows when a sea state conditionof zero exists, ie a condition whereby there is current flow but no waveaction.

If Y equals zero, i.e. float not initially submerged, the drag forces onthe float are a result of, and equal to, only those wind forces abovethe surface of the liquid. With the float not submerged, the lift due toliquid displacement is negligible and the vertical downward force willresult only from the payload or weight, P, of the float. Payload refersto the weight of the float including its contacts, but does not includethe Weight of the cable. Under this condition, the float will assumesomething less than the initial no submergence position since it mustsink at least sufliciently to support the payload or weight.

If Y equals 2R, the maximum vertical dimension of the float, then thedrag forecs on the float will be equal to the liquid currents alone andthe lift will be at a maximum because of total submergence. The ratio ofthe lift, L, to the drag D, will determine the cable angle, 15. The dragforce from the current will generally be at a maximum when Y equals oris greater than 2R because the current can operate against the entirefloat when it is fully submerged.

It is desirable to obtain a maximum ratio of lift to drag so as tominimize the inclination of the cable from its vertical position, hencemooring the float with a minimum amount of cable.

The relationship for an optimum Y is as follows:

Y, is chosen so that:

Equation 1 and:

=Density of the liquid py=DIlSltY of the gas C Drag coefficient of thefloat in the liquid for horizontal motion C :Drag coefficient of thefloat in the gas for horizontal motion V =Current velocity in the liquidV =Wind velocity in the gas B (Y :Area of float projected on a verticalplane below gas in liquid 5 (Y :Area of float projected on a verticalplane above liquid in gas and:

M (Y )=Volume of float in liquid M (Y )=Volume of float in gas =Densityof liquid Density of gas P=Payload or mass of float g=Gravity Thisrelationship for Y is valid for any size and shape of float, for anytype of liquid or gas and for any drag coefficients.

Establishment of the relationship for tension, T, and cable angle,

Having established the relationship of the float submergence, Y lift, L,and drag, D, of Step 1 we may proceed to establish the relationship forthe cable tension, T, and cable angle, in terms of L and D.

Thus:

T =L +D Equation 2 and:

L J5 tan (180-1 Equatio 3 where T=Tension of the cable at point ofattachment to float =Angle of the cable with the horizontal at point ofattachment to the float L=Lift as defined under Step 1 D==Drag asdefined under Step 1 STEP 3 Determination of T, L, D and for theflotation system:

The aforementioned parameters of T, L, D and as are now made tosimultaneously satisfy Equations 1, 2 and 3 thus resulting in fourunknowns for the three equations; however, since We may vary one of theunknowns, as for example T, we can then proceed to select and establishthe remaining three unknowns, namely the lift, L, drag, D, and cableangle, 41. The optimum tension, T, is selected applying thespecifications and requirements on system weight, non-submergence of thefloat, etc. as set forth previously.

Having now established the flotation system we combine this withestablishment of a favorable mooring system which shall be determined inStep 4.

STEP 4 Determination of cable parameters:

Having established the previous relationships and parameters for thefloat, We may proceed to select a cable having a diameter, d, and a wetweight, W, per unit length. A set of currents, V(y), are chosen at eachdepth portion, y, and upon knowing the drag coefficient of the cable wemay proceed to solve for the cable dimensions by utilizing the followingdifferential equations, expressing the equilibrium of each differentiallength of cable.

and

COS 45 =0 Equation 5 where:

T:Cable tension W=Cable wet weight per unit length =Angle between cableand motion into current measured counterclockwise from motion to cables=Cable length F=Tangential drag per unit length and where the functionof D which is the drag per unit length of cable when cable is normal tothe stream, is obtained from the following relationship:

D /2 C I d where:

C=Dimensionless drag coeflicient of cable in fluid stream =Mass densityof fluid V =Velocity of fluid d=Diarneter of cable STEP 5 Simulated testand final design:

After having established a given float system and anchorage system, thesystem is then tested in a simulated sea, in sea state ranging from seastate 0, using size 2R, starting tension, T, starting angle, startingsubmergence, Y total length, L, cable diameter, D, cable wet weight, W(per unit length), having specified currents V and wind V The system istested using simulated waves of x and y motions which involves solvingthe differential equations relating to the cable motion. The mathematicsfor the sea state condition is well established and reference may bemade to sea state chart in book entitled Waves and Beaches, pages 48-49,Table II, by Willard Bascom, published by Anchor Books, Doubleday &Company, Inc., Garden City, New York, in 1964; also Hydrographic OflicePublication No. 9, entitled American Practical Navigator by Bowditch,published in 1958, pertinent references being on page 1059, Appendix Rentitled Beaufort Scale with Corresponding Sea State Codes. The systemis tested to determine whether the float will submerge in sea state 5 orcause the cable to break in sea state 8. There is thus established afinal design of the system which combines the necessary performance andcompactness of size. The system has assurance of survival in a severestorm as well as maintaining the necessary float condition. Theforegoing design parameters are applicable to moored systems containingsubsurface floats and canisters and also applies where the cable variesalong its length in physical properties desired. The design parametersare also applicable to a nonmoored system, especially one which utilizesa long cable suspended below the float such as commonly used in sonobuoyequipments, by considering such system as being anchored by a cablewhose bottom portion has a Youngs modulus of zero.

In the design of a system in accordance with the invention, theflotation system and the mooring system are related so that optimumvalues can be obtained for the submergence, size, and shape of the floatand for an optimum diameter, weight, density, and volume of the cable.These relations are all established with environmental conditions inmind, including the sea state, wind currents, water current, etc. sothat the system will reliably function in retaining the float within aprescribed area and without breaking during various sea stateconditions. The physical parameters of the cable and of the floatcombine optimum values including air transportability, appropriate size,flotation, strength and mass so that the system will have a degree ofreliability in use not heretofore obtainable.

The arrived at system is tested in sea state conditions ranging fromtranquil to violent and the system operates so that the float remainsabove water at sea state and will survive sea state 8. Such a system isoptimum from the standpoint of performance and size and will survivereliably at its moored position.

Although the present invention has been illustrated and described inconnection with a single example embodiment, it will be understood thatthis is illustrative of the invention and is by no means restrictivethereof. It is reasonably to be expected that those skilled in this artcan make numerous revisions and adaptations of the invention, and it isintended that such revisions and adaptations will be included within thescope of the following claims as equivalents of the invention.

What is claimed is:

1. A mooring system adapted to be launched from an aircraft fordeployment in a deep water environment, said mooring system comprisinganchoring means Which is adapted to be fixed at the bottom of a body ofwater, flexible mooring means secured at one end to said anchoringmeans, a float operatively secured to the upper end of said flexiblemooring means and adapted to be movable at the surface of the waterwithin circumscribed bounds in accordance with a radius of movement froman anchored reference point provided by said anchoring means,

the distance of movement of said buoy being in accordance with adistance X determined for a given submergence distance Y and a tension Twithin the strength limitations of such cable, the relationship of theforegoing being in accordance with:

T =L +D and having a length s defined by the relations:

and

where W is the unit wet weight of said mooring means, is the anglebetween said flexible mooring means and the motion ofthe surroundingwater, F is the drag of said flexible mooring means for the surroundingconditions of the water, and D is the drag per unit length of theflexible mooring means normal to the motion of the surrounding water.

References Cited UNITED STATES PATENTS 3,005,909 10/1961 Grandoff244-136 X 412,341 10/1889 Languet 98 3,176,982 4/1965 ODaniell 98 X612,109 10/1898 Hutchins 98 3,101,491 8/1963 Salo 98 3,295,489 1/1967Bossa 98 X FERGUS S. MIDDLETON, Primary Examiner J. L. FORMAN, AssistantExaminer

